The nature of π-hole interactions between iodide anions and quinoid rings in the crystalline state

Analysis of charge density in a π-hole contact between an iodide anion and tetrabromoquinone reveals the nature of the interaction as dominantly electrostatic with a significant dispersion component. The quinoid ring has a partial negative charge (estimated to be in the range 0.08–0.11e) and a partial radical character and the energy of the interaction is estimated to be −11.16 kcal mol−1.

Even though the majority of studies have been carried out on electron-poor aromatic systems, quinoid rings, having electron-depleted carbonyl groups, are more promising acceptors of -hole interactions ( Quinones with four electronegative substituents have especially prominent -holes Vuković et al., 2019) and their interactions with halide anions often involve a charge transfer, indicated by a colour change of the compound (Molčanov et al., 2018;Milašinović & Molčanov, 2021). The common structure motif of the compound under investigation is a sandwich-like group involving two close contacts between a quinone and two halide anions, X À Á Á ÁQÁ Á ÁX À (Fig. 1). The interaction, involving charge transfer is presumably of n ! * type, and is often related to the reduction of quinones to semiquinone radicals. It may be assumed that the 'sandwich' is an intermediate in the reduction of a quinone. Owing to its common formation it may be used in crystal engineering.
However, the nature and strength of this quinone-iodide interaction remains elusive, and a detailed study is difficult. The dark colour and opacity of the crystals impede studies that use optical spectroscopy, and the presence of heavy atoms (iodine and bromine) makes quantum chemical study challenging. The strong absorption limits the applicability of X-ray diffraction studies. Our initial work (Molčanov et al., 2018) on a series of similar compounds used structural characterization that coupled infrared and solid-state NMR spectroscopies and quantum chemical computation [MP2 and periodic density functional theory (DFT)]. The results highlighted the n ! * charge transfer and estimated the interaction energy to be 6À10 kcal mol À1 (by the MP2 method). However, the degree of charge transfer remained an open issue. Most likely it is quite low (a few percent of an electron), which would be sufficient for a colour change, but not enough to be quantified by spectroscopic methods. A simple analysis of crystal structures using Hirshfeld surfaces (HSs), highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) computed using the CrystalExplorer software (Spackman et al., 2021) and analysis of Voronoi-Dirichlet polyhedra (VDP) (Blatov, 2004) confirmed this model (Milašinović & Molčanov, 2021).
In this work, we opted for a combined experimental and theoretical charge density study on a model system, a cocrystal of 3-chloro-N-methylpyridinium iodide and tetrabromoquinone [(3-Cl-N-MePy) 2 I 2 ÁBr 4 Q, named 1, Fig. 2]. To avoid absorption problems, we used short-wavelength (0.6 Å ) high-intensity synchrotron radiation for the X-ray diffraction studies. The analysis of the electron density obtained is further supported by extensive theoretical calculations both in the gas phase and as a crystalline structure. This approach allows us to study in detail the behaviour of molecular orbitals in the areas of crucial interactions, interaction energies as well as provide discussion on the topological analysis of charge density.

Crystal packing of 1
The asymmetric unit of 1 comprises a 3-Cl-N-MePy cation, an iodide anion and half of a centrosymmetric Br 4 Q molecule; therefore, the molecular formula is (3-Cl-N-MePy) 2 I 2 ÁBr 4 Q. The easily recognized motif is a sandwich-like I À Á Á ÁBr 4 QÁ Á ÁI À unit ( Fig. 1) which we have identified in similar compounds (Molčanov et al., 2018;Milašinović & Molčanov, 2021). The distance from the iodide to the centroid of the quinoid ring is 3.947 Å , the distance to the ring mean plane is 3.727 Å and the angle between the iodide-centroid axis and the ring plane is 72.0 . The iodide is offset by 1.220 Å approximately towards C2; the angle defining the direction of the offset relative to the carbonyl-carbonyl axis is 76.8 . The only contact shorter than the sum of van der Waals radii for I and C (3.76 Å ) is I1Á Á ÁC3 [3.7450 (7) Å ].
Crystal packing can be described as cations inserted between I À Á Á ÁBr 4 QÁ Á ÁI À units (Fig. 3). Aside from the -hole contact with Br 4 Q, the iodide forms three halogen bonds, two with bromine from the Br 4 Q molecules and one with a Cl from the cation (Table 1). It also forms two close contacts (3.70 Å ) with N1 and C8 atoms from the cation, which are the result of electrostatic attraction between the cation and anion.
The quinone acts as electron donor of two symmetryindependent halogen bonds (a total of four; Table 1) and its oxygen atom accepts two weak hydrogen bonds from the cation ( Table 2). A pair of inversion-related cations form astacked pair with antiparallel C-Cl bonds (Fig. S9). The interplanar separation (the ring planes are parallel, so = 0 )  Sandwich-like I À Á Á ÁBr 4 QÁ Á ÁI À unit in 1 with geometric parameters indicated. Symmetry-independent atoms are labelled.
The importance of contacts with the iodide anion is illustrated by the HS of the Br 4 Q molecule ( Fig. 4): CÁ Á ÁI contacts comprise 7.4% of the surface, whereas BrÁ Á ÁI contacts (representing halogen bonding) comprise a further 7.3%. This is slightly higher than in a previously studied series of cocrystals [where the CÁ Á ÁI contacts comprised 6-7% of the HS (Milašinović & Molčanov, 2021)]. The non-localized nature of the iodide-quinone interaction is also noted when the surface of a Br 4 Q molecule is constructed using VDP (Blatov, 2004): 12 individual faces corresponding to 12 individual CÁ Á ÁI contacts (six for each symmetry-independent CÁ Á ÁI interaction, Fig. S10) have a total area of 16.64 Å 2 or 3.5% of the VDP surface. These contact areas are similar to those found in another series of compounds [typically 6-7% of the HS and 3-3.8% of the VDP surface (Milašinović & Molčanov, 2021)].

Analysis of intermolecular electron density and iodidequinone contacts
Intermolecular critical points (Fig. 5, Table 3) are mostly in agreement with the geometric analysis of crystal packing. There are two (3, À1) critical points between the iodide and the quinoid ring, with respective electron densities of 0.040 and 0.014 e Å À3 (Table 3); the stronger one corresponds to a bond path between I1 and the most electron-depleted atom of the quinone C1 (Fig. 5). The same critical points have also been reproduced by a periodic DFT model, with somewhat higher electron densities of 0.065 and 0.042 e Å À3 , respectively (Table 3). This is consistent with the electrostatic nature of the iodide-quinone interaction, thus the covalent component is likely negligible (see below).
The analysis of theoretical charges (Table 4) indicates a partial charge transfer from the iodide to the quinoid ring of À0.077 to À0.109e, implying a partial negative charge of the Br 4 Q. This corresponds with the black colour of the crystals and confirms our previous conclusion (Molčanov et al., 2018). It also provides a more reliable estimate of the degree of charge transfer, as our previous tentative computations were severely overestimated (Molčanov et al., 2018). Therefore, the interaction is of the n ! * type donates electrons into an empty * (i.e. LUMO) orbital of the quinone, which manifests  Hirshfeld surface of a Br 4 Q molecule with closest-neighbour atoms colour coded: H -grey, C -black, O -red, Cl -green, Br -brown and Ipurple. Table 1 Short halogen-halogen distances. (4) 87.76 (5) 1 À x, 1 À y, 1 À z † Type II contact.

Figure 3
Crystal packing viewed approximately in the h100i direction. Iodide anions are shown as spheres of arbitrary radii. Table 2 Geometric parameters of hydrogen bonds.

Other intermolecular contacts
The AIM (Atoms In Molecule) analysis of intermolecular electron density shows that the highest electron density is found in halogen bonds (Table 3); for C-BrÁ Á ÁI it exceeds 0.06 e Å À3 (0.09 e Å À3 in the theoretical model), and it is slightly lower in the C-ClÁ Á ÁI bond. This is in agreement with previous studies, which showed that the strength of halogen bonding involving Br as a donor is comparable to hydrogen bonding (Stilinović et al., 2017) and that it involves a nonnegligible covalent component (Eraković et al., 2019). However, despite higher electron density, the C-BrÁ Á ÁI halogen bonds are local interactions, whereas the IÁ Á Áquinone interaction is non-localized, dispersed between several centres of the Br 4 Q molecule. Therefore, it can be concluded that the halogen bonds are of lesser importance in the crystal packing.
Hydrogen bonding (with the exception of C4-H4Á Á ÁO1) is weaker, with a maximum electron density below 0.06 e Å À3 (0.11 e Å À3 in the theoretical model, Table 3). Note that two contacts, which satisfy geometric criteria [     (7) 0.0452 0.54 (3, À1) 1 À x, 1 À y, 1 À z Table 4 Mulliken and Bader charges calculated in the gas-phase (g) as well as in a periodic system (p). Steiner, 2002)] do not have a corresponding (3, À1) critical point, therefore they should not be considered as hydrogen bonds. However, three C-HÁ Á ÁBr bonds with a DÁ Á ÁA distance exceeding 3.9 Å (Tables 2 and 3) have (3, À1) critical points with electron densities of about 0.03 e Å À3 . This discrepancy between geometric and AIM criteria for weak hydrogen bonding has been noted previously (Milašinović et al., 2020).

Conclusions
This work confirmed the nature of the iodide-quinone interaction as a -hole interaction involving n ! * charge transfer. The contact is strongly attractive (its strength and importance in crystal packing are second only to cation-anion electrostatic attraction), with an estimated interaction exceeding À11 kcal mol À1 , and its dominant component is electrostatic with a significant dispersion contribution. However, a relatively low electron density (not exceeding 0.045 e Å À3 , Table 3) found between the iodide and the quinone indicates that the interaction is not localized but dispersed between multiple centres (as shown by the HS and the VDP, Figs. 4 and S10). The estimated degree of charge transfer between the iodide and the quinone is À0.077 to À0.109 e, consistent with the black colour of the crystals.
Since -hole interactions between iodide and quinone occur frequently [so far we described more than 20 analogous compounds (Molčanov et al., 2018;Milašinović & Molčanov, 2021)], we expect that they can be employed in crystal engineering. However, since the sandwich-like moiety I À Á Á ÁBr 4 QÁ Á ÁI À is probably formed as a stable intermediate in the reduction of the quinone, it can be expected that more electronegative quinones will be reduced to radicals, while the less electronegative ones will not have sufficiently largeholes. To test the applicability of this interaction in crystal engineering, a larger number of compounds should be tested, including quinones with different substituents (with different electron-withdrawing capabilities) and different nucleophiles (bromine and other halides as well as similar anions such as cyanate, isocyanate, thiocyanate etc.).

Preparation and basic characterization
All reagents and solvents were purchased from commercial sources (Merck, Sigma-Aldrich, Kemika), were of p.a. purity and were used without further purification.

X-ray diffraction and refinement details
Single-crystal XRD data were collected at the Rossendorf Beamline [ESRF, Grenoble, France (Scheinost et al., 2021)] equipped with an Si(111) monochromator and two Pd-coated mirrors. The single-crystal data were recorded with a Pilatus3 X 2M detector ( Calculated HOMOs and LUMOs (at an isovalue of 0.001 e au À3 ) for the trimer of a tetrabromoquinone molecule and two iodine anions, located at a distance of 3.947 Å from the centroid of the quinoid ring (as observed in the crystal structure).

Figure 7
Ternary plot of the SAPT2+3 decomposition of the interaction energy between the Br 4 Q ring and two iodine anions. per 0.6200926 Å . The monochromator energy was calibrated against the first inflection of the K-absorption edge of an Mo metal foil point, tabulated as 20000 eV. The diffraction measurements were performed in shutterless mode with an angular step size of 0.1 and a counting time of 0.1 s per frame. The detector geometry parameters were calibrated with PyFAI (Kieffer & Wright, 2013) using a powder pattern of the NIST 660b standard LaB 6 . Experimental data were collected using the Pylatus software (Dyadkin et al., 2016) and treated using the SNBL ToolBox (Dyadkin et al., 2016) and CrysAlis PRO (Rigaku OD, 2019).
A total of 131 167 reflections were collected, up to a maximum of 40.9 (d = 0.475 Å ). The multiple integrated reflections were averaged for the space group P2 1 /c using SORTAV (Blessing, 1987) adapted to the area detector data.
The structure was solved using SHELXT  and a spherical-atom model was refined using SHELXL2017 . Multipolar refinement was carried out versus all reflections F 2 with the program package MoPro (Jelsch et al., 2005). Halogen atoms were modelled as hexadecapoles, O, N and C as octupoles and hydrogens as dipoles; loose restraints were used for multipoles and exponential coefficients of chemically equivalent atoms. Vibrations of halogen atoms were refined as anharmonic using fourth-order Gram-Charlier coefficients. Anisotropic parameters for hydrogen atoms were calculated by the SHADE3 server (Madsen, 2006) and kept fixed in the multipolar atom refinement; aromatic C-H bond lengths were restrained to 1.077 (2) Å and methyl CÀH bond lengths to 1.083 (2) Å . Geometry and charge-density calculations and analysis of HSs were performed using MoPro (Jelsch et al., 2005); molecular graphics were prepared using MoProViewer (Guillot, 2012) and CCDC-Mercury (Macrae et al., 2020). Crystallographic and refinement data are shown in Table 5.
The analysis of the VDP was achieved using the Topos PRO program package (Blatov, 2004).

Computational details
Gas-phase calculations were carried out in order to obtain more insight into the nature of the quinone-iodide interaction by means of molecular orbitals, atomic charges and interaction energies. Single-point DFT calculations at the B3LYP/def2-SVPD level of theory (Pritchard et al., 2019) were performed using the GAUSSIAN 16.C.01 program package (Frisch et al., 2016). Grimme D3 dispersion correction (Grimme et al., 2010) was applied in conjunction with the Becke-Johnson damping function and the core electrons for the iodide anions were approximated using pseudopotential functions (Peterson et al., 2003). Bader charges were obtained with the AIMAll software (Keith, 2019). The SAPT2+3 level was performed with the Psi4 software (version 1.3.2; Turney et al., 2012) symmetryadapted perturbation theory [SAPT (Jeziorski et al., 1994)] using the same basis set as in single-point DFT calculations.
The choice of a smaller def2-SVPD basis set was found to be a good compromise between the efficiency and accuracy of calculations performed. A benchmark study (Parker et al., 2014) found the gold standard of SAPT calculations to be the SAPT2+(3)MP2 using the aug-cc-pVTZ basis set. Unfortunately, this basis set, and the other basis sets included in the benchmark study, did not achieve SCF convergence in the single-point calculations when we tried to predict the molecular orbitals with the experimental structure of the chosen fragment, i.e. one Br 4 Q molecule and two iodine anions.  Table 5 Crystallographic data collection and charge-density refinement details. Moreover, the triple zeta basis sets would have been rather computationally expensive for SAPT calculations beyond SAPT0. Choosing a basis set that is similar to those in the above-mentioned benchmark study, we found that the def2-SVPD did achieve convergence, was small enough to complete SAPT2+3 calculations in a timely fashion and is accurate enough to describe non-covalent interactions correctly, as already discussed in the literature (Witte et al., 2016;. Although we could have extended the single-point calculations that produced the molecular orbital diagrams to a larger def2 basis set, we choose instead to keep the same level of theory for both the molecular orbital calculations and the calculation of the interaction energies. It is also important to point out here that SAPT2+3 calculations are designed to compute energies of dimers. In our studies, we chose a slightly different approach and instead of taking only one iodide anion and quinone ring for consideration, we opted for a trimer, where we treated the Br 4 Q molecule as a single unit, and two iodide anions as a second unit. Such a choice was motivated by the specific crystal packing where indeed the interaction between the quinone molecule and two iodide anions occurs simultaneously. Although such an approach is not commonly used, one may find examples in the literature when more than two units were considered (Yourdkhani et al., 2016;Steber et al., 2017).
To further support the discussion on the nature of intra-and intermolecular interactions in the crystalline state, periodic DFT was engaged with the use of the CRYSTAL17 software (Dovesi et al., 2018). Calculations were performed on the PBE0/POB-DZVP level of theory (Vilela Oliveira et al., 2019) applying an additional Grimme's D3 correction (Grimme et al., 2010). Atomic coordinates were taken from the X-ray diffraction experiment and were kept frozen during modelling. Periodic wavefunctions obtained in such a way were further used to carry out the topological analysis of periodic electron densities. The QTAIM approach was adopted (Bader, 1990) using the TOPOND14 program (Gatti & Casassa, 2017) integrated with CRYSTAL17.

Funding information
Financial support by the Croatian Science Foundation (grant no. IP-2019-04-4674) is gratefully acknowledged. This research was supported in part by PL-Grid Infrastructure (grant no. plgrhopolar1e).